Add noise to mask texture
If as mentioned in the question this is for an environment texture, we need to have a way to tune where the disk/shape will be displayed in the sky:

A possibility is to calculate the length from 2 coordinates (here X and Z), transform it eventually (square root for instance, optional) and filter using a color ramp. The length from (X,Z) is easier to tune/place than a gradient texture.
The shape orientation in the sky can be defined using a mapping node and its rotations.
The perturbation is given by a musgrave/noise combination (for instance) which displaces a bit the input coordinates.

Playing with it a bit (three settings of this kind) and mixing colors (still as world node tree):